Since 1979, it has been known that one-dimensional sound diffusive surfaces, called reflection phase gratings that scatter sound uniformly, can be formed from a series of divided wells or slats, whose depths or heights respectively, are determined according to a variety of optimal number theory sequences. In August 2016, a reference book was published titled “Acoustic Absorbers and Diffusers: Theory, Design and Application,” by authors Trevor J. Cox and Peter D'Antonio, CRC Press. In the book, it was suggested that a new type of diffuser consisting of a plurality of equally spaced, parallel rectilinear slats of equal cross-sectional width, but of differing heights, determined according to a number theory sequence, specifically a quadratic residue (QR) sequence, might be used to provide high-mid frequency diffusion and low frequency absorption.
FIG. 1 shows a schematic, side view representation of the slatted diffusing-absorbing device, based on a prime 13, QR sequence, disclosed in the above-mentioned book. No design methodology was provided. However, experimental diffusion coefficient data were presented comparing the performance of a simple prime 7, QR sequence, with a few surfaces having slats of equal height, including a regular arrangement and two irregular arrangements, based on optimal binary sequences.
At the base of the slats, a porous absorbing material is also provided, which adds resistance to the slat resonator formed by the channels between the slats. No description was provided to determine the resonant frequencies of the plurality of slat resonators. The necessity to vary the slat heights to improve dispersion is illustrated in FIG. 2.
The graphs in FIG. 2 show the normalized diffusion coefficient for the devices shown. When the device merely consists of a regularly spaced set of slats of uniform height, then at best a coefficient of 0.2 is achieved (Graph line A). Graph line B shows an irregular arrangement based on an optimal aperiodic sequence. Graph line C shows an irregular arrangement based on a periodic, truncated maximum length sequence. Two examples are shown in Graph lines B & C. While arrangements B and C show improved diffusion, at most the normalized diffusion coefficient is 0.5. However, by varying slat heights, based on a prime 7, QR sequence, the maximum diffusion coefficient is increased to almost 0.7 (Graph line D).
After further research, the present invention teaches the theory and design methodology for a practical device that can be utilized in a wide range of architectural spaces, with primes much larger than 7, which offer an aesthetic, symmetrical topology. In addition, the present invention teaches the theory to determine the resonant frequencies of the spaced slats and a number theory sequence to optimize their bandwidth, both of which are not provided by the brief suggestion made in the published book.